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45de1d006d
because different tests have different ideas about what it means to be "close enough" to the right answer, depending on the properties of the function being tested. In the process, I fixed some warnings and added a few more 'volatile' hacks, which are sufficient to make all the tests pass at -O2 with clang.
313 lines
9.8 KiB
C
313 lines
9.8 KiB
C
/*-
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* Copyright (c) 2008-2011 David Schultz <das@FreeBSD.org>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/*
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* Tests for corner cases in cexp*().
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <assert.h>
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#include <complex.h>
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#include <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#include "test-utils.h"
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#define N(i) (sizeof(i) / sizeof((i)[0]))
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#pragma STDC FENV_ACCESS ON
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#pragma STDC CX_LIMITED_RANGE OFF
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/*
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* Test that a function returns the correct value and sets the
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* exception flags correctly. The exceptmask specifies which
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* exceptions we should check. We need to be lenient for several
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* reasons, but mainly because on some architectures it's impossible
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* to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
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* whether cexp() raises an invalid exception is unspecified.
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*
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* These are macros instead of functions so that assert provides more
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* meaningful error messages.
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*
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* XXX The volatile here is to avoid gcc's bogus constant folding and work
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* around the lack of support for the FENV_ACCESS pragma.
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*/
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#define test(func, z, result, exceptmask, excepts, checksign) do { \
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volatile long double complex _d = z; \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(cfpequal_cs((func)(_d), (result), (checksign))); \
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assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
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} while (0)
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/* Test within a given tolerance. */
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#define test_tol(func, z, result, tol) do { \
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volatile long double complex _d = z; \
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assert(cfpequal_tol((func)(_d), (result), (tol), \
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FPE_ABS_ZERO | CS_BOTH)); \
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} while (0)
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/* Test all the functions that compute cexp(x). */
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#define testall(x, result, exceptmask, excepts, checksign) do { \
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test(cexp, x, result, exceptmask, excepts, checksign); \
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test(cexpf, x, result, exceptmask, excepts, checksign); \
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} while (0)
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/*
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* Test all the functions that compute cexp(x), within a given tolerance.
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* The tolerance is specified in ulps.
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*/
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#define testall_tol(x, result, tol) do { \
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test_tol(cexp, x, result, tol * DBL_ULP()); \
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test_tol(cexpf, x, result, tol * FLT_ULP()); \
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} while (0)
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/* Various finite non-zero numbers to test. */
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static const float finites[] =
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{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
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/* Tests for 0 */
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void
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test_zero(void)
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{
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/* cexp(0) = 1, no exceptions raised */
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testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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}
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/*
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* Tests for NaN. The signs of the results are indeterminate unless the
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* imaginary part is 0.
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*/
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void
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test_nan()
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{
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int i;
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/* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
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/* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
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for (i = 0; i < N(finites); i++) {
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testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
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if (finites[i] == 0.0)
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continue;
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/* XXX FE_INEXACT shouldn't be raised here */
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testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
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}
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/* cexp(NaN +- 0i) = NaN +- 0i */
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testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
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/* cexp(inf + NaN i) = inf + nan i */
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testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(-inf + NaN i) = 0 */
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testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(NaN + NaN i) = NaN + NaN i */
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testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT, 0, 0);
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}
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void
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test_inf(void)
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{
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int i;
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/* cexp(x + inf i) = NaN + NaNi and raises invalid */
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for (i = 0; i < N(finites); i++) {
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testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT, FE_INVALID, 1);
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}
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/* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
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/* XXX shouldn't raise an inexact exception */
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testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0),
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ALL_STD_EXCEPT, 0, 1);
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/* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
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/* XXX shouldn't raise an inexact exception */
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testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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/* cexp(inf + 0i) = inf + 0i */
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testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0),
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ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0),
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ALL_STD_EXCEPT, 0, 1);
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}
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void
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test_reals(void)
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{
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int i;
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for (i = 0; i < N(finites); i++) {
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/* XXX could check exceptions more meticulously */
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test(cexp, CMPLXL(finites[i], 0.0),
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CMPLXL(exp(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexp, CMPLXL(finites[i], -0.0),
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CMPLXL(exp(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexpf, CMPLXL(finites[i], 0.0),
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CMPLXL(expf(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexpf, CMPLXL(finites[i], -0.0),
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CMPLXL(expf(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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}
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}
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void
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test_imaginaries(void)
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{
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int i;
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for (i = 0; i < N(finites); i++) {
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test(cexp, CMPLXL(0.0, finites[i]),
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CMPLXL(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexp, CMPLXL(-0.0, finites[i]),
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CMPLXL(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexpf, CMPLXL(0.0, finites[i]),
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CMPLXL(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexpf, CMPLXL(-0.0, finites[i]),
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CMPLXL(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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}
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}
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void
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test_small(void)
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{
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static const double tests[] = {
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/* csqrt(a + bI) = x + yI */
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/* a b x y */
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1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
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-1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
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2.0, M_PI_2, 0.0, M_E * M_E,
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M_LN2, M_PI, -2.0, 0.0,
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};
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double a, b;
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double x, y;
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int i;
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for (i = 0; i < N(tests); i += 4) {
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a = tests[i];
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b = tests[i + 1];
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x = tests[i + 2];
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y = tests[i + 3];
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test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
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/* float doesn't have enough precision to pass these tests */
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if (x == 0 || y == 0)
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continue;
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test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
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}
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}
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/* Test inputs with a real part r that would overflow exp(r). */
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void
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test_large(void)
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{
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test_tol(cexp, CMPLXL(709.79, 0x1p-1074),
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CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
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test_tol(cexp, CMPLXL(1000, 0x1p-1074),
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CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
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test_tol(cexp, CMPLXL(1400, 0x1p-1074),
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CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
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test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020),
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CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
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test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020),
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CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
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test_tol(cexpf, CMPLXL(88.73, 0x1p-149),
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CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(90, 0x1p-149),
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CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(192, 0x1p-149),
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CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(120, 0x1.234568p-120),
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CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(170, 0x1.234568p-120),
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CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
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}
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int
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main(int argc, char *argv[])
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{
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printf("1..7\n");
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test_zero();
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printf("ok 1 - cexp zero\n");
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test_nan();
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printf("ok 2 - cexp nan\n");
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test_inf();
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printf("ok 3 - cexp inf\n");
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test_reals();
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printf("ok 4 - cexp reals\n");
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test_imaginaries();
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printf("ok 5 - cexp imaginaries\n");
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test_small();
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printf("ok 6 - cexp small\n");
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test_large();
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printf("ok 7 - cexp large\n");
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return (0);
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}
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